During development, the speed of homomorphic execution is a big blocker for fast prototyping. You could call the function you're trying to compile directly, of course, but it won't be exactly the same as FHE execution, which has a certain probability of error (see Exactness).
Considering this, simulation is introduced:
from concrete import fhe
import numpy as np
return (x + 1) ** 2
inputset = [np.random.randint(0, 10, size=(10,)) for _ in range(10)]
circuit = f.compile(inputset, p_error=0.1)
sample = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
actual = f(sample)
simulation = circuit.simulate(sample)
After the simulation runs, it prints this:
[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
[1, 4, 9, 16, 16, 36, 49, 64, 81, 100]
Currently, simulation is better than directly calling from Python, but it's not exactly the same with FHE execution. This is because it is implemented in Python.
Imagine you have an identity table lookup. It might be omitted from the generated FHE code by the Compiler, but it will still be present as optimizations are not done in Python. This will result in a bigger error in simulation.
Some operations also have multiple table lookups within them, and those cannot be simulated unless their actual implementations are ported to Python. In the future, simulation functionality will be provided by the Compiler, so all of these issues will be addressed. Until then, keep these in mind.